[VetteVet]

The next time you run the engine before you shut it down disconnect the fan power wire and then shut it off and see if the problem happens. I suspect you have wired something wrong in the power circuit. Try to give a few more details such as "the engine starts cranking" or "it runs with the key off" or how you wired the fan as has been asked.
Also disconnect the alternator and then try the engine run shut and see what happens.

The starter circuit is very simple on the 66 and all the other years for that matter. The power goes to the key switch and the key switch sends it on to the starter solenoid. I don't know for sure but I don't think some of them had neutral safety switches.